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    • I felt old as a teacher when high school students told me that they didn’t know the 3,6,9 rule. I didn’t use calculators in school until high school and remember learning that shortcut in middle school: I suppose it was more useful back then when you didn’t have a smartphone handy.

      You know, I wasn’t sure of the age range of your homeschooler, but they might enjoy this game that @Mathgarden has used with his daughter. He says that knowing prime numbers is foundational, but I just think it’s a fun and addictive little game. Don’t try to beat his high score: last I heard, he got 56 correct in one minute(!).